Generalized Interval-Valued Fuzzy Metric Spaces and their Applications

Abstract

In this paper, we have generalized the interval-valued fuzzy metric M(x,y,t) by allowing it to take the positive interval number instead of ordinary positive real number. In our case, both $t$ and the grade value M(x,y,t) are interval numbers.The underlying topology of this generalized interval-valued fuzzy metric GIVF metric is studied. Two celebrated fixed point theorems of Banach and Edelstein are extended in this space. Also the problem related to image filter processing is also studied.